Analytic motion-compensated region-of-interest reconstruction from truncated projections

The aim of this work was to propose an analytic reconstruction of two-dimensional CT images in the presence of both patient motion and truncation of the projection data. The proposed method is based on the method of differentiated backprojection with Hilbert filtering (DBP-H). There is a variant of this algorithm which suits our purpose because it begins with a simple backprojection of the unprocessed projection data. The motion correction can be achieved by incorporating an analytic deformation compensation at the backprojections step, then the algorithm proceeds as usual. A simulation experiment was performed on a slice of the Shepp Logan phantom subject to a geometry-preserving deformation. The setup was such that the solutions of the deformation problem alone or of the truncation problem alone are known, but not that of both at the same time. The results demonstrate the efficacy of our approach, and that this type of reconstruction is feasible.